Ah, it isn't called the Terrible Twos for nothing!
Actually, I see this in my wonderful granddaughters sometimes. They're well over two, but they have been known to try out this behavior on me. They can change their minds with the speed of light, and I also notice that, when A would choose one thing and B would choose the same thing, A would quickly change her mind and want something else instead! Aha - the game is on! I reduce (or eliminate) their choices; it's helpful and stress-relieving. I think a one-child version of the same game may be going on at your house.
Let your little girl make decisions sometimes, within a very limited range and a very limited time frame. At other times, you make the decisions. She may not tell you (she may not know), but she will like it that she doesn't have to decide all the time. That's a big responsibility for a little girl. We want our children to learn how to make good choices, but you know as an adult that decision-making is stressful. You have to do it every day anyway; she doesn't. Not at that age. She also needs to learn to abide by your decisions, so she's actually getting a good lesson when you choose things.
Oh, and screaming gets nothing. That part of the game needs to stop right now. Asking politely might get her what she wants; screaming NEVER will. Screaming should be saved for when the house catches fire. This means you have to stop screaming as well, but you're the grownup, so you can do that. Keep your sense of humor, and make your attitude one of friendly firmness - "I love you more than anything, AND this is the way it's going to be." She'll catch on that her game is no fun any more (and then she'll think up another one!).